Mice and seedlings

I have discovered to my cost that mice like to eat seeds and seedlings if you leave them too low down in the greenhouse. Both sweet peas and sunflowers have been lost so far. I have now moved everything up on to shelving but I am about to run out of space and I have more seedlings to prick out.

Do mice like all seeds and seedlings and if so how big do they need to be before they are safe? I have lots of small pelargoniums that I have made from cuttings and they seem to be safe on the floor.

Dont think that they wont get to the top shelves! I have lost whole trays of runner beans before when on the top shelf, they do seem to prefer the seed and young shoots, once the beans have reached a certain size they seem to be left alone.

As fidgetbones says propagator lids and mouse traps do the trick for me.